Elliptic curve isogeny class with LMFDB label 398544.s (Cremona label 398544s)

• Label: 398544.s
• Number of curves: $2$
• Conductor: $398544$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 398544.s have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(19\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 398544.s do not have complex multiplication.

Modular form 398544.2.a.s

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 398544.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
398544.s1	398544s2	\([0, -1, 0, -3276121328, 71193105772608]\)	\(55900396438928556625/875360193471018\)	\(60894146680410074355489742848\)	\([]\)	\(283668480\)	\(4.3241\)
398544.s2	398544s1	\([0, -1, 0, -342664208, -2394852841536]\)	\(63964821056640625/1396665211752\)	\(97158560444259148012879872\)	\([]\)	\(94556160\)	\(3.7748\)	\(\Gamma_0(N)\)-optimal